1-1 Characteristics of Functions

2-1 Rational Functions

3-1 Exponential Relationships

4-1 Statistics

1-2 Complex Numbers & Quadratics

2-2 Radical Functions

3-2 Trigonometric Functions

FLORIDA STATEWIDE ASSESSMENT

April 16–May 11, 2018

1-3 Polynomial Functions

2-3 Sequences and Series

3-3 Probability

Algebra 2 Mastery

Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include polynomial, rational, and radical functions.

Students work closely with the expressions that define the functions, and continue to expand and hone their abilities to model situations and to solve equations, including

solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms. The Standards for Mathematical

Practice apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject

that makes use of their ability to make sense of problem situations. The critical areas for this course, organized into four units, are as follows:

Unit 1- Polynomial, Rational, and Radical Relationships: This unit develops the structural similarities between the system of polynomials and the system of integers.

Students draw on analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students

connect multiplication of polynomials with multiplication of multi-digit integers, and division of polynomials with long division of integers. Students identify zeros of

polynomials, including complex zeros of quadratic polynomials, and make connections between zeros of polynomials and solutions of polynomial equations. The unit

culminates with the fundamental theorem of algebra. A central theme of this unit is that the arithmetic of rational expressions is governed by the same rules as the

arithmetic of rational numbers.

Unit 2- Trigonometric Functions: Building on their previous work with functions, and on their work with trigonometric ratios and circles in Geometry, students now use

the coordinate plane to extend trigonometry to model periodic phenomena.

Unit 3- Modeling with Functions: In this unit students synthesize and generalize what they have learned about a variety of function families. They extend their work with

exponential functions to include solving exponential equations with logarithms. They explore the effects of transformations on graphs of diverse functions, including

functions arising in an application, in order to abstract the general principle that transformations on a graph always have the same effect regardless of the type of the

underlying function. They identify appropriate types of functions to model a situation, they adjust parameters to improve the model, and they compare models by

analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as “the process of choosing and

using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions” is at the heart of this unit. The narrative discussion and

diagram of the modeling cycle should be considered when knowledge of functions, statistics, and geometry is applied in a modeling context.

Unit 4- Inferences and Conclusions from Data: In this unit, students see how the visual displays and summary statistics they learned in earlier grades relate to different

types of data and to probability distributions. They identify different ways of collecting data— including sample surveys, experiments, and simulations—and the role that

randomness and careful design play in the conclusions that can be drawn.

Unit 5- Applications of Probability: Building on probability concepts that began in the middle grades, students use the languages of set theory to expand their ability to

compute and interpret theoretical and experimental probabilities for compound events, attending to mutually exclusive events, independent events, and conditional

probability. Students should make use of geometric probability models wherever possible. They use probability to make informed decisions.

THE SCHOOL DISTRICT OF LEE COUNTY

Academic Plan

Algebra 2 (1200330)

Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Additional Course Information Professional Development Helpful Websites

Fluency Recommendations A-APR.6 This standard sets an expectation that students will divide polynomials with remainder by inspection in simple cases. For example, one can view the rational expression

𝑥 + 4

𝑥 + 3 𝑎𝑠

𝑥 + 4

𝑥 + 3=

(𝑥 + 3) + 1

𝑥 + 3= 1 +

1

𝑥 + 3

A-SSE.2 The ability to see structure in expressions and to use this structure to rewrite expressions is a key skill in everything from advanced factoring (e.g., grouping) to summing series to the rewriting of rational expressions to examine the end behavior of the corresponding rational function. F- IF.3 Fluency in translating between recursive definitions and closed forms is helpful when dealing with many problems involving sequences and series, with applications ranging from fitting functions to tables to problems in finance.

Math Practices for High School

Build Relationships: Teach More Than ‘Just Math’

Formative Assessment Practices to Support Student Learning: Research shows that formative assessments have a significant impact on student learning gains. This article has links to four videos to demonstrate the clarify, elicit, interpret, act formative assessment practice.

CPALMS MFAS Training

Research around formative assessment shows that students make greater learning gains when they are accountable for their own learning and the learning of their peers. The video, Facilitating Peer Learning, is a good example of a math classroom where students are engaged with one another.

Five “Key Strategies” for Effective Formative Assessment

Asking Good Questions & Promoting Discourse (Part 1).

Teaching Channel: Videos and Best Practices https://www.teachingchannel.org/

Illustrative Mathematics: Performance Tasks https://www.illustrativemathematics.org/

Inside Mathematics: Videos and Best Practices http://www.insidemathematics.org/

Khan Academy: Practice by Grade Level Standards https://www.khanacademy.org/commoncore/map

Shmoop: Math videos http://www.shmoop.com/video/math-videos

State Assessment Information

FSA Portal

Training Tests Site

Calculator & Reference Sheet Policy Reference Sheet Packet Online Testing Scientific Calculator for FSA

Algebra 2 FSA Test Item Specifications

THE SCHOOL DISTRICT OF LEE COUNTY

1-1 Academic Plan Algebra 2 (1200330)

Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Big Idea: Characteristics of Functions Standards

Math Content Standards Suggested Literacy & English Language Standards MAFS.912.F-IF.2: Interpret functions that arise in applications in terms of the context.

MAFS.912.F-IF.2.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

MAFS.912.F-IF.2.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

MAFS.912.F-IF.2.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

MAFS.912.F-BF.2: Build new functions from existing functions.

MAFS.912.F-BF.2.3: Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), and 𝑓(𝑥 + 𝑘) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

MAFS.912.F-BF.2.4: Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and

write an expression for the inverse. For example, 𝑓(𝑥) = 2 𝑥3 or 𝑓(𝑥) = (𝑥 + 1)/(𝑥– 1) for 𝑥 ≠ 1.

b. Verify by composition that one function is the inverse of another. c. Read values of an inverse function from a graph or a table, given that the function has

an inverse. d. Produce an invertible function from a non-invertible function by restricting the domain.

MAFS.912.A-CED.1: Create equations that describe numbers or relationships.

MAFS.912.A-CED.1.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

LAFS.910.SL.1.1: Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. a. Come to discussions prepared, having read and researched

material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.

b. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.

c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.

d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.

Suggested Mathematical Practice Standards MAFS.K12.MP.2.1: Reason abstractly and quantitatively.

Is there another way to write the equation or represent the problem?

Explain how the equation represents the word problem.

MAFS.912.A-CED.1.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

MAFS.912.A-REI.3: Solve systems of equations.

MAFS.912.A-REI.3.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

MAFS.912.A-REI.4: Represent and solve equations and inequalities graphically.

MAFS.912.A-REI.4.11: Explain why the 𝑥-coordinates of the points where the graphs of the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝑓(𝑥) and/or 𝑔(𝑥) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Essential Outcome Question(s) What information can be gathered from various forms of a function, and how can this information be used to transform, write, and solve problems involving functions?

Aligned Learning Goals District Adopted Materials

Supplemental Resources

Strategies for Differentiation

Define and use function vocabulary, including function, interval, end behavior, domain, range, set notation, interval notation, parameters, stretch, compression, even function, odd function, parent function, inverse function, composition of function

Understand and demonstrate how to define intervals for the domain and range of a function using inequalities, set notation, and interval notation

Graph linear functions, both with and without a restricted domain and describe their end behavior

Apply knowledge of intervals and graphing with a restricted domain to model real world situations

Apply transformations to various functions, including those with restricted domains

Find the inverse of a function

Use inverse function notation and determine if the new equation is also a function

Houghton Mifflin Module 1

Lessons 1.1, 1.2, 1.3, 1.4

FSA Item Specifications:

Algebra 2 EOC Item Specifications

THE SCHOOL DISTRICT OF LEE COUNTY

1-2 Academic Plan

Algebra 2 (1200330)

Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Big Idea: Complex Numbers & Quadratic Equations

Standards

Math Content Standards Suggested Literacy & English Language Standards MAFS.912.A-SSE.2: Write expressions in equivalent forms to solve problems.

MAFS.912.A-SSE.2.3: Choose and produce an equivalent form of an expression to reveal

and explain properties of the quantity represented by the expression. ★ a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum

value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions.

For example the expression can be rewritten as ≈ to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

MAFS.912.N-CN.1: Perform arithmetic operations with complex numbers.

MAFS.912.N-CN.1.1: Know there is a complex number 𝑖 such that 𝑖² = – 1, and every complex number has the form 𝑎 + 𝑏𝑖 with 𝑎 and 𝑏 real.

MAFS.912.N-CN.1.2: Use the relation 𝑖² = – 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

MAFS.912.N-CN.3: Use complex numbers in polynomial identities and equations.

MAFS.912.N-CN.3.7: Solve quadratic equations with real coefficients that have complex solutions.

MAFS.912.A-REI.2: Solve equations and inequalities in one variable.

MAFS.912.A-REI.2.4: Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for 𝑥² = 49), taking square roots,

completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝑎 ± 𝑏𝑖 for real numbers a and b.

MAFS.912.A-CED.1: Create equations that describe numbers or relationships.

MAFS.912.A-CED.1.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

MAFS.912.A-CED.1.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in

LAFS.1112.RST.2.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11-12 texts and topics. ELD.K12.ELL.MA.1: English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

Suggested Mathematical Practice Standards MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of others. Do you agree with that answer? Explain.

Repeat what he/she said in your own words.

How do you know what you are saying is true? MAFS.K12.MP.4.1: Model with mathematics.

What other ways could you use to model the situation mathematically?

What connections can you make between different representations of the situation?

a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

MAFS.912.F-IF.3: Analyze functions using different representations.

MAFS.912.F-IF.3.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

b. Use the properties of exponents to interpret expressions for exponential functions. MAFS.912.G-GPE.1: Translate between the geometric description and the equation for a conic section.

MAFS.912.G-GPE.1.2: Derive the equation of a parabola given a focus and directrix. MAFS.912.A-REI.3: Solve systems of equations.

MAFS.912.A-REI.3.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line 𝑦 = – 3𝑥 and the circle 𝑥² + 𝑦² = 3.

Essential Outcome Question(s)

How do key features of the graphs of quadratic functions relate to real-world situations?

Aligned Learning Goals District Adopted Materials

Supplemental Resources

Strategies for Differentiation

Define and use vocabulary associated with quadratic equations, including axis of symmetry, discriminant, parabola, quadratic formula, completing the square, vertex form, vertex, solution, intercepts, maximum, minimum, imaginary number, complex number, directrix, focus,

Identify and explain key features of the graph of a parabola in mathematical and real world contexts

Solve quadratic equations, recognizing the most efficient method to use based on the equation, including taking square roots, factoring, completing the square, and the quadratic formula

Identify whether solutions to quadratic equations are real or complex

Perform operations with imaginary numbers and complex numbers

Use the focus and directrix to write and graph the equation of a parabola

Solve a system of two equations, one linear and one quadratic

Houghton Mifflin Modules

3 & 4 Omit Lessons

4.1 & 4.4

FSA Item Specifications:

Algebra 2 EOC Item Specifications

THE SCHOOL DISTRICT OF LEE COUNTY

1-3 Academic Plan

Algebra 2 (1200330)

Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Big Idea: Polynomial Functions Standards

Math Content Standards Suggested Literacy & English Language Standards MAFS.912.A-REI.4: Represent and solve equations and inequalities graphically.

MAFS.912.A-REI.4.11: Explain why the 𝑥-coordinates of the points where the graphs of the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝑓(𝑥) and/or 𝑔(𝑥) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. (Add to Module 5)

MAFS.912.A-CED.1: Create equations that describe numbers or relationships.

MAFS.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. (Lesson 6.5)

MAFS.912.A-CED.1.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. (Lesson 7.2)

MAFS.912.F-BF.1: Build a function that models a relationship between two quantities.

MAFS.912.F-BF.1.1: Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a

context. (Lesson 5.1) b. Combine standard function types using arithmetic operations. For example, build a

function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. (Lesson 5.1)

MAFS.912.F-BF.2: Build new functions from existing functions.

MAFS.912.F-BF.2.3: Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), and 𝑓(𝑥 + 𝑘) for specific values of 𝑘 (both positive and negative); find the value of 𝑘 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (Lesson 5.1)

LAFS.1112.WHST.3.9: Draw evidence from informational texts to support analysis, reflection, and research. ELD.K12.ELL.MA.1: English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

Suggested Mathematical Practice Standards MAFS.K12.MP.4.1: Model with mathematics.

Does your solution make sense?

What do you know about the situation already? MAFS.K12.MP.6.1: Attend to precision.

How do you know your answer is accurate?

Did you use the most efficient way to solve the problem?

MAFS.912.F-IF.2: Interpret functions that arise in applications in terms of the context.

MAFS.912.F-IF.2.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. (Lessons 5.1 & 5.2)

MAFS.912.F-IF.3: Analyze functions using different representations.

MAFS.912.F-IF.3.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. (Lessons 5.1 & 5.2)

MAFS.912.A-SSE.1: Interpret the structure of expressions.

MAFS.912.A-SSE.1.1: Interpret expressions that represent a quantity in terms of its context. (Lesson 6.5) a. Interpret parts of an expression, such as terms, factors, and coefficients.

MAFS.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it. For example, see 𝑥4 − 𝑦4 as (𝑥2)2 − (𝑦2)2, thus recognizing it as a difference of squares that can be factored as (𝑥2 𝑦2)(𝑥2 + 𝑦2). (Add to Lesson 6.5)

MAFS.912.A-APR.1: Perform arithmetic operations on polynomials.

MAFS.912.A-APR.1.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (Lessons 6.5 & 7.2)

MAFS.912.A-APR.2: Understand the relationship between zeros and factors of polynomials.

MAFS.912.A-APR.2.2: Know and apply the Remainder Theorem: For a polynomial 𝑝(𝑥) and a number 𝑎, the remainder on division by 𝑥 − 𝑎 is 𝑝(𝑎), so 𝑝(𝑎) = 0 if and only if (𝑥 −𝑎) is a factor of 𝑝(𝑥). (Lesson 7.2)

MAFS.912.A-APR.2.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. (Lessons 6.5 & 7.2)

MAFS.912.A-APR.3: Use polynomial identities to solve problems.

MAFS.912.A-APR.3.4: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (𝑥2 + 𝑦2)2 = (𝑥2 − 𝑦2)2 + (2𝑥𝑦)2 can be used to generate Pythagorean triples. (Add to Module 6)

MAFS.912.A-APR.4: Rewrite rational expressions.

MAFS.912.A-APR.4.6: Rewrite simple rational expressions in different forms; write 𝑎(𝑥)/𝑏(𝑥) in the form 𝑞(𝑥) + 𝑟(𝑥)/𝑏(𝑥), where 𝑎(𝑥), 𝑏(𝑥), 𝑞(𝑥), and 𝑟(𝑥) are polynomials with the degree of 𝑟(𝑥) less than the degree of 𝑏(𝑥), using inspection, long division, or, for the more complicated examples, a computer algebra system. (Lesson 6.5)

Essential Outcome Question(s)

What similarities and differences exist between cubic equations and quadratic equations?

Aligned Learning Goals District Adopted Materials

Supplemental Resources

Strategies for Differentiation

Identify the attributes of a polynomial function of degree three or more, including domain, range, end behavior, increasing and decreasing intervals, zeros, and if the function is even or odd

Graph cubic equations, applying various transformations

Sketch the graph of various polynomial functions, with and without technology, identifying zeros, turning points, end behavior, intercepts, maximums, and minimums

Extend understanding of factoring polynomial expressions to include the sum and difference of two cubes

Fluently factor, write, and divide polynomials in different forms to best model a given situation

Use long division, synthetic division, and computer applications to divide polynomials

Understand and apply the Remainder Theorem when dividing polynomials

Find the zeros of a polynomial function with integer coefficients and use zeros to write a polynomial function

Houghton Mifflin Modules 5, 6, & 7

Omit Lessons 6.1, 6. 2, 6.3, 6.4, 7.2

FSA Item Specifications:

Algebra 2 EOC Item Specifications

THE SCHOOL DISTRICT OF LEE COUNTY

2-1 Academic Plan Algebra 2 (1200330)

Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Big Idea: Rational Functions Standards

Math Content Standards Suggested Literacy & English Language Standards MAFS.912.F-IF.3: Analyze functions using different representations.

MAFS.912.F-IF.3.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

d. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. (Lesson 8.1)

MAFS.912.F-BF.2: Build new functions from existing functions.

MAFS.912.F-BF.2.3: Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), and 𝑓(𝑥 + 𝑘) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (Lesson 8.1)

MAFS.912.F-BF.2.4: Find inverse functions. (Lesson 8.1) a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and

write an expression for the inverse. For example, f(x) =2 x³ or f(x) = (x+1)/(x–1) for x ≠ 1. b. Verify by composition that one function is the inverse of another. c. Read values of an inverse function from a graph or a table, given that the function has

an inverse. d. Produce an invertible function from a non-invertible function by restricting the domain.

MAFS.912.A-SSE.1: Interpret the structure of expressions.

MAFS.912.A-SSE.1.1: Interpret expressions that represent a quantity in terms of its context. b. Interpret complicated expressions by viewing one or more of their parts as a single

entity. For example, interpret 𝑃(1 + 𝑟)𝑛 as the product of P and a factor not depending on 𝑃. (Lesson 9.3)

MAFS.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it. For example, see 𝑥4 − 𝑦4 as (𝑥2)2 − (𝑦2)2, thus recognizing it as a difference of squares that can be factored as (𝑥2 − 𝑦2)(𝑥2 + 𝑦2). (Lesson 9.3)

MAFS.912.F-BF.1: Build a function that models a relationship between two quantities.

MAFS.912.F-BF.1.1: Write a function that describes a relationship between two quantities.

LAFS.1112.WHST.3.9 Draw evidence from informational texts to support analysis, reflection, and research. LAFS.910.SL.2.4: Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. ELD.K12.ELL.MA.1: English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

Suggested Mathematical Practice Standards MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning.

What generalizations can you make?

Can you find a shortcut to solve the problem? How would your shortcut make the problem easier?

MAFS.K12.MP.6.1: Attend to precision.

How do you know your answer is accurate?

b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. (Lessons 8.1 & 8.2)

MAFS.912.F-IF.2: Interpret functions that arise in applications in terms of the context.

MAFS.912.F-IF.2.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. (Lessons 8.1 & 8.2)

MAFS.912.A-REI.1: Understand solving equations as a process of reasoning and explain the reasoning.

MAFS.912.A-REI.1.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (Lesson 9.3)

MAFS.912.A-REI.1.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. (Lesson 9.3)

MAFS.912.A-CED.1: Create equations that describe numbers or relationships.

MAFS.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. (Add to Module 9)

MAFS.912.A-CED.1.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. (Lessons 8.1, 8.2, & 9.3)

Essential Outcome Question(s)

What information about polynomials and graphs of functions do you know that you can apply to rational expressions and functions?

Aligned Learning Goals District Adopted Materials

Supplemental Resources

Strategies for Differentiation

Identify the attributes of a rational function, including domain, and vertical and horizontal asymptotes

Analyze and graph rational functions, identifying key features and any points of discontinuity

Rewrite rational expressions in different forms and recognize equivalent forms of rational expressions

Houghton Mifflin Modules

8 & 9 Omit 9.1 & 9.2

Rewrite rational expressions to create a simplified expression

Solve rational equations and identify extraneous solutions

Solve rational equations, identifying any extraneous solutions

FSA Item Specifications:

Algebra 2 EOC Item Specifications

THE SCHOOL DISTRICT OF LEE COUNTY

2-2 Academic Plan Algebra 2 (1200330)

Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Big Idea: Radical Functions Standards

Math Content Standards Suggested Literacy & English Language Standards MAFS.912.A-CED.1: Create equations that describe numbers or relationships.

MAFS.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.

MAFS.912.A-CED.1.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (Add to Module 11)

MAFS.912.F-BF.2: Build new functions from existing functions.

MAFS.912.F-BF.2.3: Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), and 𝑓(𝑥 + 𝑘) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (Lesson 10.2)

MAFS.912.F-BF.2.4: Find inverse functions. (Lesson 10.1 & 10.2) a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and

write an expression for the inverse. For example, f(x) =2 x³ or f(x) = (x+1)/(x–1) for x ≠ 1. b. Verify by composition that one function is the inverse of another. c. Read values of an inverse function from a graph or a table, given that the function has an

inverse. d. Produce an invertible function from a non-invertible function by restricting the domain.

MAFS.912.F-IF.2: Interpret functions that arise in applications in terms of the context.

MAFS.912.F-IF.2.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. (Lesson 10.2)

MAFS.912.F-IF.3: Analyze functions using different representations.

MAFS.912.F-IF.3.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. b. Graph square root, cube root, and piecewise-defined functions, including step functions

and absolute value functions. (Lessons 10.2, 10.3, & 11.2)

LAFS.1112.WHST.2.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. ELD.K12.ELL.MA.1: English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

Suggested Mathematical Practice Standards MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them.

What is this problem asking?

Could someone else understand how to solve the problem based on your explanation?

MAFS.K12.MP.5.1: Use appropriate tools strategically.

What math tools are available for finding the solution to a system of equations or inequalities?

MAFS.912.N-RN.1: Extend the properties of exponents to rational exponents.

MAFS.912.N-RN.1.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define to be the cube root of 5 because we want = to hold, so must equal 5. (Lesson 11.1)

MAFS.912.N-RN.1.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. (Lesson 11.2)

MAFS.912.A-REI.1: Understand solving equations as a process of reasoning and explain the reasoning.

MAFS.912.A-REI.1.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (Lesson 11.3)

MAFS.912.A-REI.1.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. (Lesson 11.3)

Essential Outcome Question(s)

How are radicals and rational exponents related?

Aligned Learning Goals District Adopted Materials

Supplemental Resources

Strategies for Differentiation

Find and graph the inverse of quadratic and cubic functions

Understand and explain why the inverse of a quadratic function is the square root function and the inverse of a cubic function is the cube root function

Explain why restricting domains may be necessary when finding the inverse of a function and verify inverses using composition of functions

Analyze square root and cube root functions, identifying key features, including domain, range, and parent graph

Graph square root and cube root functions and apply knowledge of transformations when graphing

Identify transformations of parent graphs of square root and cube root functions given as an equation

Use square root and cube root functions to model and solve real world problems

Simplify expressions with rational exponents

Solve radical equations, identifying any extraneous solutions

Use radical equations to model and solve real world problems

Houghton Mifflin Modules 10 & 11

FSA Item Specifications:

Algebra 2 EOC Item Specifications

THE SCHOOL DISTRICT OF LEE COUNTY

2-3

Academic Plan

Algebra 2 (1200330) Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Big Idea: Sequences and Series Standards

Math Content Standards Suggested Literacy & English Language Standards MAFS.912.F-BF.1: Build a function that models a relationship between two quantities.

MAFS.912.F-BF.1.1: Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a

context.

MAFS.912.F-BF.1.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

MAFS.912.A-SSE.1: Interpret the structure of expressions.

MAFS.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it. For example, see 𝑥4 − 𝑦4 as (𝑥2)2 − (𝑦2)2, thus recognizing it as a difference of squares that can be factored as (𝑥2 − 𝑦2)(𝑥2 + 𝑦2).

MAFS.912.A-SSE.2.4: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate

mortgage payments. ★ MAFS.912.A-CED.1: Create equations that describe numbers or relationships.

MAFS.912.A-CED.1.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

MAFS.912.F-IF.3: Analyze functions using different representations.

MAFS.912.F-IF.3.7: Graph functions expressed symbolically and show key features of the

graph, by hand in simple cases and using technology for more complicated cases. ★ e. Graph exponential and logarithmic functions, showing intercepts and end behavior,

and trigonometric functions, showing period, midline, and amplitude, and using phase shift.

LAFS.1112.RST.1.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text. LAFS.1112.SL.1.2: Integrate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, orally) in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data. ELD.K12.ELL.MA.1: English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

Suggested Mathematical Practice Standards MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them.

How can you use an easier form of the problem to help make sense of it?

MAFS.K12.MP.7.1: Look for and make use of structure.

How can you apply what you know about key features of graphs to make sense of equations in various forms?

Essential Outcome Question(s)

How do sequences and series help to solve real-world problems?

Aligned Learning Goals District Adopted Materials

Supplemental Resources

Strategies for Differentiation

Understand and explain the difference between an explicit rule and a recursive rule for sequences

Identify and write arithmetic and geometric sequences, both explicitly and recursively

Graph arithmetic and geometric sequences

Use arithmetic and geometric sequences to model and solve real world problems

Define geometric series and derive a formula for finding the sum of a finite geometric series

Find the sum of a finite geometric series

Use geometric series to model and solve real world problems

Houghton Mifflin Modules

12

FSA Item Specifications:

Algebra 2 EOC Item Specifications

THE SCHOOL DISTRICT OF LEE COUNTY

3-1

Academic Plan Algebra 2 (1200330)

Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Big Idea: Exponential Relationships Standards

Math Content Standards Suggested Literacy & English Language Standards MAFS.912.F-BF.2: Build new functions from existing functions.

MAFS.912.F-BF.2.3: Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), and 𝑓(𝑥 + 𝑘) for specific values of 𝑘 (both positive and negative); find the value of 𝑘 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (Lesson 13.1, 13.2, & 13.3)

MAFS.912.F-IF.2: Interpret functions that arise in applications in terms of the context.

MAFS.912.F-IF.2.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. (Lesson 13.3)

MAFS.912.F-IF.3: Analyze functions using different representations.

MAFS.912.F-IF.3.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and

trigonometric functions, showing period, midline, and amplitude, and using phase shift. (Lesson 13.3)

MAFS.912.F-IF.3.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

MAFS.912.F-LE.1: Construct and compare linear, quadratic, and exponential models and solve problems.

LAFS.1112.RST.1.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text. LAFS.1112.SL.1.2: Integrate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, orally) in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data. ELD.K12.ELL.MA.1: English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

Suggested Mathematical Practice Standards MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them.

How can you use an easier form of the problem to help make sense of it?

MAFS.K12.MP.5.1: Use appropriate tools strategically.

Is using a calculator or mental math more appropriate for this situation?

How could you estimate the problem to check your work?

MAFS.912.F-LE.1.4: For exponential models, express as a logarithm the solution to 𝑎𝑏𝑐𝑡 = 𝑑 where 𝑎, 𝑐, and 𝑑 are numbers and the base 𝑏 is 2, 10, or 𝑒; evaluate the logarithm using technology.

MAFS.912.A-SSE.1: Interpret the structure of expressions.

MAFS.912.A-SSE.1.1: Interpret expressions that represent a quantity in terms of its context. (Lesson 13.4) a. Interpret complicated expressions by viewing one or more of their parts as a single

entity. For example, interpret 𝑃(1 + 𝑟)𝑛 as the product of P and a factor not depending on 𝑃. (Lesson 9.3)

MAFS.912.A-SSE.2: Write expressions in equivalent forms to solve problems.

MAFS.912.A-SSE.2.3: Choose and produce an equivalent form of an expression to reveal

and explain properties of the quantity represented by the expression. ★ b. Use the properties of exponents to transform expressions for exponential functions. For

example the expression can be rewritten as (1.151

12)12𝑡 ≈ 1.01212𝑡 to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. (Lesson 13.4)

MAFS.912.A-REI.4: Represent and solve equations and inequalities graphically.

MAFS.912.A-REI.4.11: Explain why the 𝑥-coordinates of the points where the graphs of the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝑓(𝑥) and/or 𝑔(𝑥) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. (Lesson 13.3 & 13.4)

MAFS.912.A-CED.1: Create equations that describe numbers or relationships.

MAFS.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. (Lesson 16.2)

Essential Outcome Question(s)

What are the similarities and differences between exponential and logarithmic functions?

Aligned Learning Goals District Adopted Materials

Supplemental Resources

Strategies for Differentiation

Identify the attributes of the graph of an exponential function, including domain, range, asymptote, and transformations of the parent function

Write and graph exponential functions, including exponential growth, exponential decay, and base e functions, and use them to model and solve real world problems

Identify the growth rate and growth factor for an exponential growth function

Apply knowledge of exponential functions to compound interest

Houghton Mifflin Modules

13, 15, & 16

Identify the inverse of the graph of an exponential function as a logarithmic function

Convert between logarithmic and exponential equations

Evaluate logarithmic expressions algebraically and using technology

Define and evaluate natural logs, ln, using technology

Graph logarithmic functions, identifying key features, including domain, range, asymptotes, increasing and decreasing intervals, positive and negative intervals, and intercepts

Identify and apply transformations of the parent graph for a logarithmic function

Use logarithmic equations to model and solve real world problems

Know the properties of logarithms and use them to simplify logarithmic expressions

Apply properties of logarithms to rewrite logarithmic and exponential equations and solve real world problems

FSA Item Specifications:

Algebra 2 EOC Item Specifications

THE SCHOOL DISTRICT OF LEE COUNTY

3-2 Academic Plan Algebra 2 (1200330)

Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Big Idea: Trigonometric Functions Standards

Math Content Standards Suggested Literacy & English Language Standards MAFS.912.F-TF.1: Extend the domain of trigonometric functions using the unit circle.

MAFS.912.F-TF.1.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; Convert between degrees and radians. (Lesson 17.1)

MAFS.912.F-TF.1.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. (Lesson 17.2)

MAFS.912.F-TF.2: Model periodic phenomena with trigonometric functions.

MAFS.912.F-TF.2.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. (Lesson 18.4)

MAFS.912.F-TF.3: Prove and apply trigonometric identities.

MAFS.912.F-TF.3.8: Prove the Pythagorean identity 𝑠𝑖𝑛2Ɵ + 𝑐𝑜𝑠2Ɵ = 1 and use it to find 𝑠𝑖𝑛Ɵ, 𝑐𝑜𝑠Ɵ, or 𝑡𝑎𝑛Ɵ given sin, cos or tan and the quadrant of the angle. (Lesson 17.3)

MAFS.912.F-IF.2: Interpret functions that arise in applications in terms of the context.

MAFS.912.F-IF.2.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. (Lesson 18.1, 18.3, & 18.4)

MAFS.912.F-IF.3: Analyze functions using different representations.

MAFS.912.F-IF.3.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. e. Graph exponential and logarithmic functions, showing intercepts and end behavior,

and trigonometric functions, showing period, midline, and amplitude, and using phase shift. (Lessons 18.1, 18.2, 18.3, & 18.4)

LAFS.910.SL.1.2 Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source. ELD.K12.ELL.MA.1: English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

Suggested Mathematical Practice Standards MAFS.K12.MP.4.1: Model with mathematics.

Does your solution make sense?

What do you know about the situation already? MAFS.K12.MP.6.1: Attend to precision.

How do you know your answer is accurate?

MAFS.912.F-IF.3.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. (Lesson 18.2)

MAFS.912.F-BF.2: Build new functions from existing functions.

MAFS.912.F-BF.2.3: Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), and 𝑓(𝑥 + 𝑘) for specific values of 𝑘 (both positive and negative); find the value of 𝑘 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (Lesson 18.2)

MAFS.912.A-REI.4: Represent and solve equations and inequalities graphically.

MAFS.912.A-REI.4.11: Explain why the 𝑥-coordinates of the points where the graphs of the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝑓(𝑥) and/or 𝑔(𝑥) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. (Lesson 18.4)

Essential Outcome Question(s)

What are the trigonometric functions and their relationship to the unit circle and right triangle?

Aligned Learning Goals District Adopted Materials

Supplemental Resources

Strategies for Differentiation

Define and use vocabulary related to the unit circle and radian measure, including angle of rotation, standard position, initial side, terminal side, coterminal angles, reference angle, unit circle, and radian measure

Sketch and find angles of rotation and coterminal angles

Explain how to find radian measure and convert between degree measure and radian measure

Apply knowledge of basic trigonometric functions and special right triangles to the unit circle and angle of rotation

Evaluate trig functions using reference angles and quadrants, both algebraically and with technology

Understand and define the domain and range for sine, cosine, and tangent when defining these functions using the unit circle

Prove the Pythagorean Identity

Houghton Mifflin Modules 17 & 18

Use the Pythagorean Identity and sin 𝜃 , cos 𝜃, or tan 𝜃 to find the value of other trigonometric functions

Write and graph sine, cosine, secant, and cosecant functions, identifying period, midline, and amplitude

Write and graph tangent functions, identifying period, midline, amplitude, and asymptotes

Identify and perform transformations when graphing trigonometric functions

Use the sine function to model periodic phenomena

FSA Item Specifications:

Algebra 2 EOC Item Specifications

THE SCHOOL DISTRICT OF LEE COUNTY

3-3 Academic Plan Algebra 2 (1200330)

Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Big Idea: Probability Standards

Math Content Standards Suggested Literacy & English Language Standards MAFS.912.S-CP.1: Understand independence and conditional probability and use them to interpret data.

MAFS.912.S-CP.1.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). (Lesson 19.1)

MAFS.912.S-CP.1.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. (Lesson 20.2)

MAFS.912.S-CP.1.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. (Lessons 20.1, 20.2, & 20.3)

MAFS.912.S-CP.1.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. (Lessons 19.4, 20.1, 20.2, & 20.3)

MAFS.912.S-CP.1.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. (Lessons 20.1, 20.2, & 20.3)

MAFS.912.S-CP.2: Use the rules of probability to compute probabilities of compound events in a uniform probability model.

LAFS.1112.RST.3.7: Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. LAFS.910.SL.1.2: Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source. LAFS.1112.SL.2.4: Present information, findings, and supporting evidence, conveying a clear and distinct perspective, such that listeners can follow the line of reasoning, alternative or opposing perspectives are addressed, and the organization, development, substance, and style are appropriate to purpose, audience, and a range of formal and informal tasks. ELD.K12.ELL.MA.1: English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

Suggested Mathematical Practice Standards MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them.

Does this make sense?

MAFS.K12.MP.4.1: Model with mathematics.

Why do the results make sense?

Is this working or do you need to change your model?

MAFS.912.S-CP.2.6: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. (Lesson 20.1)

MAFS.912.S-CP.2.7: Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. (Lesson 19.4)

Essential Outcome Question(s)

How does probability help us to make informed decisions?

Aligned Learning Goals District Adopted Materials

Supplemental Resources

Strategies for Differentiation

Define and use vocabulary associated with probability, including element, set, empty set, universal set, set notation, subset, intersection, union, complement, Venn diagram, outcome, sample space, theoretical probability, experimental probability, factorial, mutually exclusive events, overlapping events, conditional probability, independent events, permutation, and combination

Describe events as subsets of a sample space, or as unions, intersections, or complements of other events

Calculate the theoretical probability and the complement of various events and use to solve real world problems

Recognize events that are mutually exclusive or overlapping and find the probability of these events

Use a two-way frequency table or relative frequency table to find probabilities, including conditional probability

Determine if two events are independent, and find the probability of independent events

Determine if two or more events are dependent, and find the probability of dependent events, including when there are three or more events

Understand what a fair decision is and use probability to make fair decisions

Create and interpret two-way frequency tables to analyze decisions

Houghton Mifflin Modules 19 & 20

Omit Lessons 19.2,

19.3, 20.3

FSA Item Specifications:

Algebra 2 EOC Item Specifications

THE SCHOOL DISTRICT OF LEE COUNTY

4-1 Academic Plan

Algebra 2 (1200330)

Adopted Instructional Materials: Houghton Mifflin Harcourt Algebra 2

Big Idea: Statistics Standards

Math Content Standards Suggested Literacy & English Language Standards MAFS.912.S-IC.1: Understand and evaluate random processes underlying statistical experiments.

MAFS.912.S-IC.1.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. (Lesson 22.1 & 23.1)

MAFS.912.S-IC.1.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

MAFS.912.S-IC.2: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

MAFS.912.S-IC.2.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. (Lesson 24.2)

MAFS.912.S-IC.2.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. (Lessons 23.3 & 24.1) MAFS.912.S-IC.2.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. (Lesson 24.3) MAFS.912.S-IC.2.6: Evaluate reports based on data. (Lesson 24.2)

MAFS.912.S-ID.1: Summarize, represent, and interpret data on a single count or measurement variable.

MAFS.912.S-ID.1.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. (Lessons 22.2 & 23.2)

LAFS.1112.WHST.1.1: Write arguments focused on discipline-specific content. a. Introduce precise, knowledgeable claim(s), establish the

significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences the claim(s), counterclaims, reasons, and evidence.

b. Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form that anticipates the audience’s knowledge level, concerns, values, and possible biases.

c. Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.

d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

e. Provide a concluding statement or section that follows from or supports the argument presented.

LAFS.1112.SL.1.3: Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, assessing the stance, premises, links among ideas, word choice, points of emphasis, and tone used.

Suggested Mathematical Practice Standards

MAFS.912.S-CP.2: Use the rules of probability to compute probabilities of compound events in a uniform probability model.

MAFS.912.S-CP.2.7: Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. (Lesson 23.1)

MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of others.

What conclusions can you draw, using data as your evidence?

What do you think about ____’s thinking?

Essential Outcome Question(s)

In what ways can sets of data be represented by statistics?

Aligned Learning Goals District Adopted Materials

Supplemental Resources

Strategies for Differentiation

Define and use vocabulary associated with data collection and analysis, including population, sampling, census, parameter, statistic, representative sample, biased samples, numerical data, categorical data, distribution, normal distribution, uniform distribution, skewed distribution, random variable, probability distribution, standard deviation, normal curve, z-score, margin of error, confidence interval, survey, experiment, observational study,

Distinguish among different types of sampling and research methods and determine if the method is biased and/or effective

Use simulations to generate data based on probabilities and determine if the simulation is consistent with the theoretical probability

Understand how a normal curve is created and use various methods to find the area under a normal curve

Calculate the z-score and use it to compare a single data point to the population or to compare two data points

Define and understand confidence intervals and margins of error and their role in data analysis

Find a confidence interval and margin of error for a population mean or proportion

Houghton Mifflin Modules

22, 23, & 24

FSA Item Specifications:

Algebra 2 EOC Item Specifications